Question

The profit, in thousands of dollars, from the sale of thousand candles can be estimated by P(x) = 3x -0.5x Inx. Complete parts (a) through (c). a) Find the marginal profit, p'(x) P'(x)=0 b) Find P'(77), and explain what this number represents P'(I)- (Type an integer or decimal rounded to the nearest thousandth as needed) What does P'(77) represent? O A The additional profit, in thousands of dollars, when 77,000 candles are sold OB. The additional profilin thousands of dollars, for selling a thousand candles once 77,000 candies have already been sold OC. The additional cost, in thousands of dollars, to produce 77,000 candles O D. The additional cost. In thousands of dollars, to produce a thousand candles once 77,000 candies have already been sold c) How many thousands of candles should be sold to maximize profit? (Type an integer or decimal rounded to the nearest thousandth as needed.)

Answer 1

Solution : Profit P(x) = bu-oe5n lux diffrengate PCR) with respect for So [& Cul) Well you tudi kota and chan-] p'cres = f (3x -0.5x lvm) Th pliny = 3-05 (1 + enx) T plere) = 2.5-0.5 line put x=77 ă 0.328 thousand dollarg /plers = 2+5 -0.5 ln(72) = 0.328 097289 p 'Cat) representa The additional profit in thore, ando f dollars, when I looo candles are sold